József Solymosi is a Hungarian-Canadian mathematician and a professor of mathematics at the

University of British Columbia The University of British Columbia (UBC) is a Public university, public research university with campuses near University of British Columbia Vancouver, Vancouver and University of British Columbia Okanagan, Kelowna, in British Columbia, Canada ...

. His main research interests are

arithmetic combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations ...

discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geom ...

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

, and

combinatorial number theory In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (a ...

Education and career

Solymosi earned his master's degree in 1999 under the supervision of László Székely from the

Eötvös Loránd University Eötvös Loránd University (, ELTE, also known as ''University of Budapest'') is a Hungarian public research university based in Budapest. Founded in 1635, ELTE is one of the largest and most prestigious public higher education institutions in ...

and his Ph.D. in 2001 at

ETH Zürich ETH Zurich (; ) is a public university in Zurich, Switzerland. Founded in 1854 with the stated mission to educate engineers and scientists, the university focuses primarily on science, technology, engineering, and mathematics. ETH Zurich ra ...

under the supervision of

Emo Welzl Emmerich (Emo) Welzl (born 4 August 1958 in Linz, Austria)Curriculum vitae
retrieved 2012-02-11. is a ...

. His doctoral dissertation was ''Ramsey-Type Results on Planar Geometric Objects''. From 2001 to 2003 he was S. E. Warschawski Assistant Professor of Mathematics at the

University of California, San Diego The University of California, San Diego (UC San Diego in communications material, formerly and colloquially UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California, United States. Es ...

. He joined the faculty of the University of British Columbia in 2002. He was

editor in chief An editor-in-chief (EIC), also known as lead editor or chief editor, is a publication's editorial leader who has final responsibility for its operations and policies. The editor-in-chief heads all departments of the organization and is held account ...

of the ''

Electronic Journal of Combinatorics The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin (Geor ...

'' from 2013 to 2015.

Contributions

Solymosi was the first online contributor to the first

Polymath Project The Polymath Project is a collaboration among mathematicians to solve important and difficult mathematical problems by coordinating many mathematicians to communicate with each other on finding the best route to the solution. The project began in J ...

, set by

Timothy Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a director of research at the University of Cambridge and a Fellow of Trinity College, Camb ...

to find improvements to the

Hales–Jewett theorem In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial ...

. One of his theorems states that if a finite set of points in the

Euclidean plane In mathematics, a Euclidean plane is a Euclidean space of Two-dimensional space, dimension two, denoted \textbf^2 or \mathbb^2. It is a geometric space in which two real numbers are required to determine the position (geometry), position of eac ...

has every pair of points at an integer distance from each other, then the set must have a

diameter In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest Chord (geometry), chord of the circle. Both definitions a ...

(largest distance) that is linear in the number of points. This result is connected to the

Erdős–Anning theorem The Erdős–Anning theorem states that, whenever an Infinite set, infinite number of points in the plane all have integer distances, the points lie on a straight line. The same result holds in higher dimensional Euclidean spaces. The theorem ca ...

, according to which an infinite set of points with integer distances must lie on one line. In connection with the related Erdős–Ulam problem, on the existence of dense subsets of the plane for which all distances are rational numbers, Solymosi and de Zeeuw proved that every infinite rational-distance set must either be dense in the

Zariski topology In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. It is very different from topologies that are commonly used in real or complex analysis; in particular, it is not ...

or it must have all but finitely many of its points on a single line or circle. With

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician, Fields medalist, and professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins Chair in the Co ...

, Solymosi proved a bound of

(mn)^

on the number of incidences between

n

points and

m

affine subspaces of any finite-dimensional Euclidean space, whenever each pair of subspaces has at most one point of intersection. This generalizes the

Szemerédi–Trotter theorem The Szemerédi–Trotter theorem is a mathematical result in the field of Discrete geometry. It asserts that given points and lines in the Euclidean plane, the number of incidences (''i.e.'', the number of point-line pairs, such that the point ...

on points and lines in the Euclidean plane, and because of this the exponent of

2/3

cannot be improved. Their theorem solves (up to the

\varepsilon

in the exponent) a conjecture of Toth, and was inspired by an analogue of the Szemerédi–Trotter theorem for lines in the

complex plane In mathematics, the complex plane is the plane (geometry), plane formed by the complex numbers, with a Cartesian coordinate system such that the horizontal -axis, called the real axis, is formed by the real numbers, and the vertical -axis, call ...

. He has also contributed improved bounds for the

Erdős–Szemerédi theorem In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of the sets and (the sets of pairwise sums and pairwise products, respectively) form a significantly larger set. More precis ...

, showing that every set of real numbers has either a large set of pairwise sums or a large set of pairwise products, and for the

Erdős distinct distances problem In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly-linear number of distinct distances. It was posed by Paul Erdős in 1946 and almost proven by Larry Guth and Nets Katz in 2015. ...

, showing that every set of points in the plane has many different pairwise distances.

Recognition

In 2006, Solymosi received a

Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...

and in 2008 he was awarded the André Aisenstadt Mathematics Prize. In 2012 he was named a doctor of the

Hungarian Academy of Science The Hungarian Academy of Sciences ( , MTA) is Hungary’s foremost and most prestigious learned society. Its headquarters are located along the banks of the Danube in Budapest, between Széchenyi rakpart and Akadémia utca. The Academy's primar ...

Selected publications

References

External links

Home page
* {{DEFAULTSORT:Solymosi, Jozsef Year of birth missing (living people) Living people Canadian mathematicians 20th-century Hungarian mathematicians 21st-century Hungarian mathematicians Eötvös Loránd University alumni ETH Zurich alumni Academic staff of the University of British Columbia Combinatorialists Graph theorists